Script - How to disable the cursor?
Your code hides the cursor. Nothing more nothing less. It just contains quite a lot of unnecessary "decoration". 

This is the core of the code:

import bge
bge.render.showMouse(False)


As it says it hides the cursor. 

It does not make your game ignore the mouse input. You didn't mentioned how your game deals with mouse input. Therefore you get a very generic answer:


let your logic ignore the mouse input


When you provide more details you might get a more specific answer that fits your current situation.

Recommendation


  ... the cursor to be disabled to prevent the game from clicking other menu buttons ...


I suggest you disable "clicking". There are many options to do so:


remove the clickable object (when you need clicking again - add another clickable object)
add a sensor that indicate if clicking is active or not e.g. via property

switch states to enable/disable clicking